An ant moved for several seconds and covered 3 mm in the first second and 4 mm more in each successive second than in its predecessor. If the ant had covered 1 mm in the first second and 8 mm more in each successive second, then the difference between the path it would cover during the same time and the actual path would be more than 6 mm but less than 30 mm. Find the time for which the ant moved (in seconds).a)5 sb)4 sc)6 sd)2 sCorrect answer is option 'B'. Can you explain this answer?

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An ant moved for several seconds and covered 3 mm in the first second and 4 mm more in each successive second than in its predecessor. If the ant had covered 1 mm in the first second and 8 mm more in each successive second, then the difference between the path it would cover during the same time and the actual path would be more than 6 mm but less than 30 mm. Find the time for which the ant moved (in seconds).

a)
5 s
b)
4 s
c)
6 s
d)
2 s

Correct answer is option 'B'. Can you explain this answer?

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An ant moved for several seconds and covered 3 mm in the first second ...

The movement of the ant in the two cases would be 3, 7, 11, 15, 19, 23 and 1, 9, 17, 25, 33, 41.
It can be seen that after 3 seconds the difference is 6mm, after 4 seconds, the difference is 16mm and after 5 seconds the difference is 30 mm.
Thus, it is clearly seen that the ant moved for 4 seconds.

Answered by Wizius Careers · View profile

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An ant moved for several seconds and covered 3 mm in the first second ...

To solve this problem, let's break it down into two parts:

Part 1: Ant's path with the given conditions
In the first scenario, the ant covered 3 mm in the first second and 4 mm more in each successive second than the previous second. We can represent the distance covered by the ant in each second as follows:

1st second: 3 mm
2nd second: 3 + 4 = 7 mm
3rd second: 7 + 4 = 11 mm
4th second: 11 + 4 = 15 mm
5th second: 15 + 4 = 19 mm

So, in 5 seconds, the ant would cover a total distance of 3 + 7 + 11 + 15 + 19 = 55 mm.

Part 2: Ant's path with the altered conditions
In the second scenario, the ant covered 1 mm in the first second and 8 mm more in each successive second than the previous second. We can represent the distance covered by the ant in each second as follows:

1st second: 1 mm
2nd second: 1 + 8 = 9 mm
3rd second: 9 + 8 = 17 mm
4th second: 17 + 8 = 25 mm

So, in 4 seconds, the ant would cover a total distance of 1 + 9 + 17 + 25 = 52 mm.

Comparison and Finding the Time
The difference between the two paths is 55 mm - 52 mm = 3 mm. Since the difference is less than 6 mm, the time taken by the ant must be less than 5 seconds.

However, the difference is also greater than 30 mm, so the time taken by the ant must be greater than 4 seconds.

Therefore, the correct answer is option B) 4 seconds.

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